{
  "id": 15971874,
  "title": "(B5) is empty: 420 solver-checked classes, and A(7) <= 8 now comes down to (B6)",
  "url": "https://urgent.news/2026/10/21/b5-is-empty-420-solver-checked-classes-and-a-7-8-now-comes-down-to-b6",
  "topic": "tech",
  "section": "Tech",
  "published": "2026-10-21T23:51:54.000Z",
  "source": {
    "name": "Dev.to",
    "slug": "dev-to",
    "url": "https://dev.to/munimv2/b5-is-empty-420-solver-checked-classes-and-a7-8-now-comes-down-to-b6-4lcd"
  },
  "original_language": "en",
  "account": "The research explores finite 2-groups with central involutions and their dimensions, as well as anisotropic systems over finite fields. The progression of results shows that A(6) = 6, A(7) = 9, and A(8) = 11. The focus shifts to A(7) = 8, which is now contingent on the emptiness of (B6). This paper confirms that (B5) is empty, using SAT solvers and computer-assisted methods. The solution to (B6) is currently unknown, with 68 classes remaining open.",
  "summary": "This is from MV2's open notebook on Kakeya-type problems ( https://github.com/munimtechnologies/kakeya-small-fields ). It continues the earlier posts on finite 2-groups whose involutions are all central: is such a group at most |Omega_1|^(e+1), where 2^e is its exponent? The question comes down to a number A(t), the largest dimension of an anisotropic system over F_2^t, and A(t) = t for every t…",
  "key_points": [
    "A(6) equals 6, A(7) equals 9, and A(8) equals 11",
    "(B5) confirmed empty using SAT solvers and computer-assisted methods",
    "(B6) emptiness unknown, 68 classes remain open"
  ],
  "editors_take": "The confirmation of an empty B5 set narrows the remaining mathematical uncertainty to a specific set of sixty-eight open classes within the B6 category.",
  "illustration": null,
  "coverage": {
    "outlets": 1,
    "also_reported_by": []
  },
  "ai_generated": true,
  "disclaimer": "Summaries, key points and the editor’s take are written by software from other outlets’ reporting and may contain errors — always check the linked original."
}